Question

Express 48 as a product of prime numbers using exponents. Responses 22 × 3 × 4 22 × 3 × 4 - no response given 2 × 3 × 23 2 × 3 × 23 - no response given 3 × 42 3 × 42 - no response given 24 × 3

Answer 1

To express 48 as a product of prime numbers using exponents, we can start by factoring 48:

1. Divide by 2 (the smallest prime):
\( 48 ÷ 2 = 24 \)
\( 48 = 2 × 24 \)

2. Repeat with 24:
\( 24 ÷ 2 = 12 \)
\( 24 = 2 × 12 \)
So, \( 48 = 2 × 2 × 12 \)

3. Repeat with 12:
\( 12 ÷ 2 = 6 \)
\( 12 = 2 × 6 \)
So, \( 48 = 2 × 2 × 2 × 6 \)

4. Repeat with 6:
\( 6 ÷ 2 = 3 \)
\( 6 = 2 × 3 \)
So, \( 48 = 2 × 2 × 2 × 2 × 3 \)

Now that we have fully factored 48, we can count the number of times each prime factor appears:

- The prime factor 2 appears 4 times.
- The prime factor 3 appears 1 time.

Therefore, we can write 48 as a product of primes using exponents:

\[
48 = 2^4 × 3^1
\]

So the final answer is:

\[
48 = 2^4 × 3
\]